论文标题
奇数指标
ODD Metrics
论文作者
论文摘要
我们介绍了奇数的概念（'$ \ mathbf {o} $ rthogonally $ \ mathbf {d} $在$ \ mathbf {d} $ ivisor'）riemannian riemannian指标上进行真实的分析歧管$ m $。这些半阳性的对称$ 2 $ 2次镜头可能会在有限的子手机集合中退化，而它们对这些子手法的限制则满足了归纳兼容性标准再次成为一个奇怪的度量标准。在有关这些指标的一系列文章中的第一篇文章中，我们表明它们满足了Riemannian指标所具有的基本属性。例如，我们介绍了正规框架，索引的降低和升高，奇数形式和Levi-Civita连接。我们最终表明，一个奇数诱导了$ m $的度量空间结构，至少在退化基因座的一般点$ \ mathcal {d} $，奇数向量字段是可集成的，并且存在奇怪的地理位置，并且是唯一的。
We introduce the concept of ODD ('$\mathbf{O}$rthogonally $\mathbf{D}$egenerating on a $\mathbf{D}$ivisor') Riemannian metrics on real analytic manifolds $M$. These semipositive symmetric $2$-tensors may degenerate on a finite collection of submanifolds, while their restrictions to these submanifolds satisfy the inductive compatibility criterion to be an ODD metric again. In this first in a series of articles on these metrics, we show that they satisfy basic properties that hold for Riemannian metrics. For example, we introduce orthonormal frames, the lowering and raising of indices, ODD volume forms and the Levi-Civita connection. We finally show that an ODD metric induces a metric space structure on $M$ and that at least at general points of the degeneracy locus $\mathcal{D}$, ODD vector fields are integrable and ODD geodesics exist and are unique.
